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Quantum Size Effects in Metallic Nanostructures
Michael C. Tringides
Iowa State University, Ames
Mieczyslaw Jalochowski
Maria Curie-Sklodowska University, Lublin, Poland
Ernst Bauer
Arizona State University, Tempe
In solid-state physics, crystals are usually assumed to be large enough that
the influence of finite dimensions on their electronic structure is
negligible compared to the effects of the periodic potential produced by the
regular arrangement of the ion cores. The energy of a nearly free valence-
band electron in a metal can then simply be described by its dependence on
the wave vector k = (27pi/lambda)e, where e is a unit vector in the
direction of propagation of the electron and lambda is its wavelength.
doi:10.1063/1.2731973 Physics Today，60（2007）50-54
In solid-state physics, crystals are usually assumed to be large enough that
the influence of finite dimensions on their electronic structure is
negligible compared to the effects of the periodic potential produced by the
regular arrangement of the ion cores. The energy of a nearly free valence-
band electron in a metal can then simply be described by its dependence on
the wave vector k = (2π/λ)e, where e is a unit vector in the direction of
propagation of the electron and λ is its wavelength.
When one or more dimensions of the crystal approach interatomic distances or
the electron's wavelength, however, the electron feels the effects of the
crystal boundaries in addition to the periodic potential. The potential
outside the solid is drastically different from the one inside. The
influence of the boundaries is clearest in the context of the jellium model,
in which the positive ion cores are eared out as a homogeneous positive
background. Inside the solid, the electron energy E(k) follows a simple
parabolic form. The role of the boundaries is to severely restrict the
allowed wave vectors that electrons can adopt inside the crystal.
Ultrathin films, two-dimensional islands, and one-dimensional wires can be
prepared using epitaxial methods and can exhibit what are known as quantum
size effects (QSEs) that arise from the
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